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A039825
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Floor( (n^2+n+8) / 4 ).
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0
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2, 3, 5, 7, 9, 12, 16, 20, 24, 29, 35, 41, 47, 54, 62, 70, 78, 87, 97, 107, 117, 128, 140, 152, 164, 177, 191, 205, 219, 234, 250, 266, 282, 299, 317, 335, 353, 372, 392, 412, 432, 453, 475, 497, 519, 542, 566, 590, 614, 639
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Number of different coefficient values in expansion of Product (1+q^2+q^4...+q^(2i)), i=1 to n.
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FORMULA
| The given terms have a second difference that is periodic with the period 1, 0, 0, 1, ... of length 4, an implicit recurrence - John W. Layman (layman(AT)math.vt.edu), Jan 23 2001
a(n)=Sum_{k=0..n}{(1/12)*((k mod 4)+4*((k+1) mod 4)+((k+2) mod 4)-2*((k+3) mod 4))}+a(n-1), with a(0)=2. - Paolo P. Lava (paoloplava(AT)gmail.com), Aug 24 2007
O.g.f.: -x*(-3*x+2*x^4+4*x^2-4*x^3+2)/((x-1)^3*(x^2+1)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
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MATHEMATICA
| Table[Floor[(((n*(n+1)+2)/2+1)/2+1)], {n, 5!}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 26 2010]
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CROSSREFS
| Sequence in context: A059290 A133231 A074752 * A126256 A062438 A102424
Adjacent sequences: A039822 A039823 A039824 * A039826 A039827 A039828
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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